In the manufacture of integrated circuits, photolithography, or lithography, is typically used to transfer patterns relating to the layout of an integrated circuit onto a wafer substrate, including, but not limited to, materials such as silicon, silicon germanium (SiGe), silicon-on-insulator (SOI), or various combinations thereof. The drive to improve performance of very-large-scale integrated (VLSI) circuit-s results in increasing requirements to decrease the size of features and increase the density of layouts. This in turn increasingly requires the use of Resolution Enhancement Techniques (RET) to extend the capabilities of optical lithographic processes. RET includes but not limited to techniques such as the use of optical proximity correction (OPC), sub resolution assist feature (SRAF) enhanced lithography and phase-shifted-mask-enhanced lithography (PSM).
In spite of the spectacular advancement of several forms of Resolution Enhancement Techniques (RET), the iterative Model-Based Optical Proximity Correction (MBOPC) methodology has established itself as a method of choice for compensation of the mask shapes for lithographic process effects during the process of designing such masks. Conventional MBOPC tools work include the following steps in a manner similar to the following. The shapes on the mask design (henceforth referred to as the mask) are typically defined as polygons. A pre-processing step is performed that divides the edges of each mask shape into smaller line segments. At the heart of the MBOPC tool is a simulator that simulates the image intensity at a particular point, which is typically at the center of each of the line segments. The segments are then moved back and forth, i.e., outward or inward from the feature interior, from their original position on the mask shape at each iteration-step of the MBOPC. The iteration stops when (as a result of the modification of the mask shapes) the image intensity at these pre-selected points matches a threshold intensity level, within a tolerance limit.
The aforementioned methodology is illustrated in FIG. 1. In the current state of the art, an input mask layout 101 and a target image 106 are provided. The mask shapes are divided into segments 102, where each segment is provided with a self-contained evaluation point (103). The optical and the resist image are then evaluated at evaluation points 104. In step 105, the images at each of the evaluation points are then checked against the tolerance of the target image 106. If the image does not remain within tolerance the segment is iteratively moved forward or backward 107 until all segments reside within an accepted tolerance. Eventually, the final corrected mask layout is outputted 108.
Modeling aerial images is a crucial component of semiconductor manufacturing. Since present lithographic tools employ partially coherent illumination, such modeling is computationally intensive for all but the most elementary patterns. The aerial image generated by the mask, i.e., the light intensity of an optical projection system image plane, is a critically important parameter in micro-lithography for governing how well a developed photo-resist structure replicates a mask design and which, generally, needs to be computed to an accuracy of better than 1%. Such image models are used not only in mask correction (e.g. optical proximity correction methodologies) but also in other applications, such as mask verification methodologies. Mask verification is performed on a final mask design, after modification for example by optical proximity correction, to ensure that the final image will meet specified tolerances and not exhibit any catastrophic conditions such as opens, shorts, and the like.
In an Aerial Image simulator, in addition to the diffraction of light in the presence of low order aberrations, the scattered light which affects the exposure over long distances on the wafer are recently being considered. Such long-range optical effects are generally referred to as “flare” in the literature. Flare affects the current extremely tight requirements on Across-Chip-Line-Width-Variation (ACLV). The flare effects are more pronounced in some novel RET methods requiring dual exposure such as alternating Phase Shifting Masks (Alt-PSM) or Double Di-Pole methodologies. The problem is even more pronounced in bright field masks that are used in printing critical levels which control the ultimate performance of the circuit, such as gate and diffusion levels.
One significant difficulty when taking into consideration long range effects, such as flare, is the extent of the corrections flare effects required on the mask. The diffraction effects and corresponding optical lens aberrations that are modeled by the 37 lowest order Zernikes that dies off within a range of a few microns. The flare effect, on the other hand, extends up to a few mms, thus covering the entire chip area.
Flare is generally considered to be the undesired image component generated by high frequency phase “ripples” in the wavefront corresponding to the optical process. Flare thus arises when light is forward scattered by appreciable angles due to phase irregularities in the lens. (An additional component of flare arises from a two-fold process of backscatter followed by re-scatter in the forward direction, as will be discussed hereinafter). High frequency wavefront irregularities are often neglected for three reasons. First, the wavefront data is sometimes taken with a low-resolution interferometer. Moreover, it may be reconstructed using an algorithm of an even lower resolution. Second, even when the power spectrum of the wavefront is known or inferred, it is not possible to include the effect of high frequency wavefront components on an image integral that is truncated at a short ROI distance, causing most of the scattered light to be neglected. Finally, it is not straightforward to include these terms in the calculated image. The present invention addresses these problems.
It is generally observed that the flare energy F({right arrow over (r)}) from a wavefront ripple follows approximately the inverse power law relationship of the form given by: F({right arrow over (r)})=K/({right arrow over (r)}−{right arrow over (r)})γ, where {right arrow over (r)} is the location of the point of interest influenced by the flare energy, {right arrow over (r)}′ is the location of the source of flare, K is a constant to be fitted and the exponent γ is referred to as the flare kernel parameter and is determined experimentally. Flare energy is proportional to 1/dose. An example of a plot of flare observed experimental data points 201 is shown in FIG. 2A. FIG. 2A is a dimensionless plot of flare energy as a function of distance from the source of light for a typical optical process of a numerical aperture (NA) of 0.75 and a pupil size (σ) of 0.3. The curve 202 fitted to the data points 201 yields a value for γ of 1.85.
In order to compute the impact of the flare on the image intensity at a point the flare kernel is convolved or integrated with the mask shapes. The convolved contribution of the mask shapes are summed up to get the image intensity at a point. This step is shown in FIG. 2B.
FIG. 2B is a simplified flowchart illustration of a method of simulating or recreating an output wafer image as is known in the art using the flare kernel described above. As is known in the art, method 200 provides a mask layout 201 and a set of flare parameters 202 as inputs. Parameters 202 may include for example the flare kernel parameter γ, the wavelength λ of the light used, source parameters such as inner and outer radius σ1 and σ2 of the source pupil, numerical aperture NA, and Zernike parameters Z1, Z2, . . . , Zn that define the lens aberrations of the optical system.
In order to simulate optical image intensity at a point 251, method 200 considers at step 203 an flare interaction region, or region of influence ROI, 252 surrounding the simulation point 251. Interaction region 252 may typically be a square or circular area having dimensions of typically in the range 5-20 microns across that encloses all shapes that will have a significant optical influence on the image intensity at the simulation point 251. As is known in the art, the size of the interaction region 252 is normally determined by the tradeoff between computational-speed versus desired accuracy. The image computation may typically proceed by computing the coherent kernels (Block 204), which are convolved with each of the mask functions (Block 205), and the convolutions are summed (Block 206) to obtain the simulated image on the wafer plane (Block 207).
Since the effect of flare diminishes slowly but steadily across the chip, some prior arts make certain trade offs in computing the convolution process. The most accurate of the computation is the convolution with the actual geometry of the mask shapes. However, this methodology is very slow. On the other hand the impact of flare diminishes considerably beyond 10-15 microns. Beyond this range the geometric details of the mask shapes can be approximated by a density map or a pixelated image of the geometric shapes. In the closer range (less than 1-2 microns), however, it is important to use the exact polygonal shapes for the accuracy of the image computation. Since exact polygonal shapes are used in any case for computing the diffraction limited part of the aerial image for this range of 1-3 microns, short range computation of the flare does not add to any significant runtime penalty.
Referring to FIG. 3A, a layout 30 is shown for describing pixilated or density map, whereby the layout 30 has thereon a plurality of finite geometrical shapes 31. The cell array layout 30 is divided or partitioned into a plurality of uniform patterns, illustrated as uniform rectangles 34. Other pixel shapes may be used; for example, the cell array layout 30 may be partitioned into any type of polygon pattern that is capable of spanning and covering the whole layout including, but not limited to, regular or irregular, convex or concave, or any combination thereof.
Once the layout 30 is divided into the plurality of uniform squares 34, a density map 40 of the layout may be computed, as shown in FIG. 3B. This is accomplished by initially dividing the layout 30 into each of the plurality of individual squares 34 followed by determining that portion of each square 34 that is covered by any finite geometrical shape(s) 31. Once the amount of coverage of each of the uniform squares 34 has been computed, each square 34 is then assigned a number based upon how much of that square is covered by finite geometrical shape(s) 31. For example, as shown in FIG. 3B the percentage of coverage of each square is illustrated, whereby this percentage represents a density number 45 for each square.
In accordance with the invention, the overall density map may represent numerous different density effects including, but not limited to, geometries of the finite geometrical shapes, the coverage of such geometries (e.g., the percentage of the present model-based hierarchal prime cell level that is covered by finite geometrical shapes versus that portion not covered by such shapes, such as that shown in FIG. 3B), the amount of coverage of the cell array layout 30 portion, area coverage, coverage by the computed aerial, resist or any other form of wafer image, perimeter coverage or any other topological coverage, and even combinations thereof.
After the overall density map 40 of the prime cell level is complete, i.e., once all density numbers 45 for the plurality of squares 34 have been computed, the density map 40 represents qausi-images of the shapes, rather then using exact geometries. Each density 45 operating at each of the plurality of squares 34 are convolved with the inverse power law kernel to obtain a plurality of convolved operating densities across the density map.
The geometric convolution is described with the help of FIGS. 4A, 4B, 4C, 4D. FIG. 4A shows a rectangular shape 400. FIG. 4B shows the same rectangular shape partitioned into 4 sectors, viz. 401, 402, 403 and 404. An example of a sector is shown as 450. Each of these sectors are bounded by one horizontal and one vertical line. Rectangle 400 can be expressed as the follows:
Sector 401−Sector 402−Sector 403+Sector 404. In a geometric convolution each of these sectors are convolved with the flare kernel.
The number of sectors for a shape is linearly proportional to the number of vertices of that shape. This is explained in FIGS. 4C and 4D. FIG. 4C shows a polygon 410 with 10 vertices. FIG. 4D shows the corresponding shape in terms of sectors. Shape 410 can be parsed in terms of sectors as: (Sector 411−Sector 412−Sector 413+Sector 414)+(Sector 415−Sector 416−Sector 417+Sector 418)+(Sector 419−Sector 420−Sector 421+Sector 422).
Therefore, as the number of vertices increases in a shape the geometric convolution becomes more and more computationally expensive since the number of sectors increases.
The differences between the pixel based and geometry based approach are further elaborated using FIGS. 6A and 6B. FIG. 6A shows an exemplary mask 600 with 4 micron×4 micron area with vertices A, B, C and D. The distance between vertices A and B, B and C, C and D, and, D and A are 4 microns. Mask 600 consists of 4 copies of the shape 601 at the shown locations, so that the distance between them is 605. Shape 601 is an ortho-normal shape with edges parallel to the x and the y axes only. In this example 605 has a value of 0.700 micron. The left most shape 601 is placed at a distance of 606 from the edge AD and at a distance 607 from the edge AB, respectively, of mask 600. In this example 606 has a value of 0.350 micron and 607 has a value of 0.500 microns respectively. Shape 601 have 12 vertices, viz., a, b, c, d, e, f, g, h, i, j, k, l. In this particular example, the distances between respective vertices are given as follows: a and b: 0.295 micron, b and c: 0.300 micron, c and d: 0.005 micron, d and e: 0.300 micron, e and f: 0.005 micron, f and g: 2 micron, g and h: 0.005 micron, h and i: 0.300 micron, i and j: 0.005 micron, j and k: 0.300 micron and k and l: 0.295 micron.
The shapes in mask 600 are used to compute the flare intensity at a point 606 at the center of the edge AD of the mask 600. The flare kernel is shown as the curve 610 which is an inverse power-law kernel with the value of γ=1.5.
Using geometric convolutions as explained above requires that each shape 601 of the mask is represented by 12 sectors. Therefore after 48 convolution computations (for 4 shapes) the value of the flare intensity as computed at point 606 is 0.032692. The above computation is the most accurate computation barring numerical errors.
FIG. 6B shows the effect of pixelization of the mask 600. Mask 600 is pixelized into 16 pixels, viz., 621 through 636. Each pixel size is 1 micron×1 micron. The density values of the pixels are as follows: For pixels 621, 622, 623, 624: 0.2153; For pixels 625, 626, 627, 628: 0.4456; For pixels 629, 630, 631, 632: 0.4785; and For pixels 633, 634, 635, 636: 0.1675. Using the above pixelized representation, the flare intensity at point 606 is computed as 0.029103. This result has a 10% error and uses 16 convolutions. If the pixels are made smaller the error reduces, but the number of convolution computation increases.
There is a region that is in between the short and the long range, for example, between from 2-10 microns. This region is referred to as the “Intermediate Range.” It is important to make a very careful speed accuracy trade off for the computation in this region. There are several reasons, why intermediate-range computation of flare is very important. With better optics (high gamma) intermediate range flare dominates the longer range. Accuracy is more important for the intermediate range than the longer range.
There are known methods using the density based approach or a pixelated polygons in the intermediate region for obtaining efficient computation, but that have the disadvantage of diminished accuracy. Yet other methods use exact mask geometries for accuracy at the significant cost of computational efficiency. Intermediate range flare dominates the flare computation both memory and runtime wise more than the short or the long range flares.
Accordingly, it would be desirable to provide a method for computing the convolution of intermediate range flares with mask shapes in a manner that improves the efficiency of lithographic process models for use in MBOPC or mask verification, while not reducing the quality or accuracy of the simulations.